Mathematics & Physics 2016, 9(4), 485–497 УДК 539.3, 531.3, 001.891.573 Models of Deformation of Stiffened Orthotropic Shells under Dynamic Loading Alexey A.Semenov∗ Saint Petersburg State University of Architecture and Civil Engineering 2nd Krasnoarmeyskaya, 4, Saint Petersburg, 190005 Russia Received 23.03.2016, received in revised form 02.08.2016, accepted 08.09.2016 Two models of deformation of reinforced orthotropic shells under dynamic loading are considered in this paper. <...> One such model is in the form of equations of motion and another model is in the form of a system of ordinary differential equations. <...> They take into account the geometric nonlinearity, orthotropic material properties and reinforcement elements. <...> All relations of the models are in general form, and they can be used for a wide range of structures (shallow shells of double curvature, cylindrical, conical, spherical and toroidal shells and panels, etc.). <...> The second model is derived by applying the Kantorovich method to the functional of the total energy of deformation of a shell. <...> The resulting initial value problem is easier to solve than the system of equations of motion in partial derivatives. <...> Keywords: mathematical model, shell, dynamic loading, orthotropy, geometric nonlinearity, the equations of motion, method of constructive anisotropy. <...> During the first three decades researchers dealt mainly with static problems in the theory of thin plates and shells. <...> The most studied is the behaviour of single-layer isotropic shell structures under dynamic loading. <...> In the last decade, structures fabricated of composite materials are of great interest. <...> For example, such materials as carbon fibre reinforced epoxy resin, graphite-fiber reinforced and boron-fiber reinforced plastics are widely used. <...> The main objectives of the study of shell structures under dynamic loading are to investigate their stability, strength and vibrations as evidenced by review articles and monographs [13–23]. ∗sw.semenov@gmail.com ⃝ Siberian Federal University. <...> All rights reserved c – 485 – Alexey A.Semenov Models of Deformation of Stiffened Orthotropic Shells under Dynamic Loading One should mention the extensive review article of E. A.Kogan and A.A.Yurchenko [13] which is devoted to free and forced nonlinear oscillations of multilayered thin elastic plates and shells under periodic loading. <...> As for geometry of structures, the vast majority <...>